Electromagnetic Theory and Computation: A Topological Approach: 48 (Mathematical Sciences Research Institute Publications)

Book Details:

• Publisher: Cambridge University Press

• Author: P. Robert Kotiuga

• Language: English

• Edition: 1st Edition

• ISBN: 9780521801607

• Pages: 284

• Binding: Hardcover

• Dimensions: 9.3 x 6.3 x 0.9 inches

About The Book:

Topology in Electromagnetic Field Computation by P. Robert Kotiuga explores the significant role topology plays in solving electromagnetic boundary value problems, an idea initially recognized by Gauss and Maxwell but not fully exploited until recently. This book presents a modern approach to computational electromagnetics by linking algebraic topology, data structures, algorithms, and field computation.

The first chapters provide an introduction to the relevant concepts of homology and cohomology, emphasizing their interpretations in the context of electromagnetism. Kotiuga then ties these topological structures to variational formulations in electromagnetics, the finite element method, algorithms, and numerical linear algebra. A central theme throughout the book is the development of algorithms for addressing the problem of making branch cuts, which are essential for computing magnetic scalar potentials and eddy currents.

This book provides a unique approach by marrying the theoretical aspects of topology with practical applications in electromagnetic computations. It is a valuable resource for graduate students, researchers, and professionals working in computational electromagnetics, numerical methods, and applied mathematics.